A124876 Number of prime factors (counted with multiplicity) in factorization of A007408(n).

0, 2, 1, 3, 2, 4, 3, 2, 3, 5, 3, 3, 3, 2, 1, 4, 2, 5, 1, 3, 2, 6, 2, 4, 2, 1, 3, 5, 3, 6, 1, 2, 3, 2, 3, 10, 4, 4, 5, 5, 8, 7, 7, 2, 4, 7, 3, 2, 4, 3, 2, 5, 3, 4, 2, 8, 3, 4, 4, 5, 3, 3, 7, 2, 5, 10, 4, 2, 6, 8, 3, 6, 6, 4, 3, 6, 4, 7, 4, 4, 3, 4, 8, 5, 7, 4

Offset: 1

Author

M. F. Hasler, Nov 11 2006

Keywords

• nonn

Examples

			a(1) = 0 since A007408(1) = 1 contains no prime factor,
a(2) = 2 since A007408(2) = 9 = 3 * 3,
a(3) = 1 since A007408(3) = 251 is prime,
a(6) = 4 since A007408(6) = 7 * 7 * 11 * 53.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..106

Crossrefs

Cf. A001222, A007408, A124877, A124787.

Programs

Maple

seq( add(op(2,j),j=op(2,(ifactors@A007408)(n))), n=1..28 );
A001222 := proc(n) numtheory[bigomega](n) ; end: b := fscanf("b007408.txt","%d %d") : while b <> [] do printf("%d, ",A001222(op(2,b))) ; b := fscanf("b007408.txt","%d %d") : od : # R. J. Mathar, May 18 2007

Mathematica

Table[PrimeOmega[Numerator[Sum[1/k^3, {k, 1, n}]]], {n, 1, 50}] (* Amiram Eldar, Feb 09 2020 *)
PrimeOmega[Numerator[Accumulate[1/Range[50]^3]]] (* Harvey P. Dale, Aug 28 2023 *)

Formula

a(n) = A001222(A007408(n)). - R. J. Mathar, May 18 2007

Extensions

More terms from R. J. Mathar, May 18 2007

More terms from Amiram Eldar, Feb 09 2020